Angular Displacement

To show that one cannot regard finite angular displacement as a vector quantity because the additions of such rotations do not obey the commutative law.

Large textbook, large wooden dice.

Choose two rotations for the textbook. Call these rotations O1 and O2 respectively. Performing the rotations, show that O1 + O2 does not equal O2 + O1. In such cases, the final positions of the book are quite different. It should be mentioned that infinitesimal angular displacements do add commutatively, hence angular velocities and accelerations do behave like vectors. The large pair of dice may also be used to illustrate this principle.